At the beginning of a planning period, the container yard manager must decide on the initial distribution of yard cranes among the yard blocks. The initial assignment of yard cranes can be simply random or uniformly distributed among the blocks. However, a more reasonable assignment will be that based on work volume forecasts in the blocks at the beginning of a planning period. The studies in literature dealing with the inter-block deployment problem assumes that an initial assignment of the cranes are given or known (which, in reality, is usually based on the judgement of the yard manager). However, in our study we have investigated some intuitive strategies that can be employed for the initial assignment. These strategies are presented in this section. Note that a good strategy shall be tailored to achieve objectives such as: 1) assign cranes to blocks where they are most needed i.e. based on work volume and 2) reduce the number of future inter-block crane transfers during operation to prevent loss of time and crane productivity. We address these goals in three approaches namely ‘high to low work volume’,
‘crane at each block’, and ‘reduce transfers’.
For illustration we use the following variable definitions-
Tc ≡Capacity of a cranec in time units (length of planning period)
IWb ≡Initial work volume of a block bat the beginning of a planning period NCinitialb ≡Number of cranes initially assigned to a block bat the beginning of a planning period
NCcurrentb ≡ Number of cranes currently assigned to a blockb ı.e. its value may change over operational hours
NCmaxb ≡Maximum number of cranes that can work in a block bsimultaneously (The value of NCmaxb is set to 2 in our model)
High to low work volume In this strategy, a list of blocks is generated by sorting the blocks in the order of decreasing IWb. Thus, the topmost item of the list has the maximum work volume and the bottommost item has the minimum work volume. Then, cranes are assigned to blocks according to their order in the list starting with the topmost item. Once a block is assigned NCbmax cranes, the next block in the list is considered for assignment, and the process is continued until all available cranes are assigned. Note that this simple strategy does not directly take into account the actual value of work volumes but only their relative order in the list.
Crane at each block In this strategy three possible scenarios are considered. Let total number of cranes benc and total number of blocks benb.
• If nc =nb, assign a single crane at each block.
• If nc < nb, generate a list of blocks sorted in order of decreasing IWb. Then assign a single crane to each of the topnc blocks from that list.
incomplete work volume for all blocks using Equation 4.2.
Incomplete work volume of block b= IWb−Tc (4.2)
Now, create a list of blocks sorted in decreasing order ofincomplete work volumeas found from Equation 4.2. Next assign a single crane to each of top nc−nb blocks from that list.
Reduce transfers This strategy assign cranes to blocks in following steps-
• Find the blocks that satisfy Equation 4.3. For these blocks, assign NCbmax cranes in each block.
IWb ≥ NCbmax×Tc (4.3)
• Next, find the blocks that satisfy Equation 4.4. For these blocks, assign a single crane in each block.
IWb < NCbmax×Tc and IWb ≥Tc (4.4)
• Calculate the incomplete work volume for the blocks using the following Equation 4.5.
Incomplete work volume of block b =IWb−Tc×NCbcurrent (4.5)
Then, find the blocks that satisfy the following condition in Equation 4.6.
NCcurrentb <NCbmax and Incomplete work volume of block b≥0.7×Tc (4.6) Next, create a list of these blocks sorted in order of decreasing work volume as found in Equation 4.5. Assign a single crane to each block from top of that list and continue until there are cranes available. Note that the factor ‘0.7’ in Equation 4.6 is a measure of how much need there
is for a block to have an additional crane. This factor should be between 0.66 to 1.0. For our study we used 0.7 which produces the best results in our model.
• If additional unassigned cranes are available, compute the revised in- complete work volume for blocks using Equation 4.5. Then create a list of these blocks sorted in order of decreasing work volume for which Equation 4.7 holds true.
Currently assigned number of cranes< NCmaxb (4.7) Next assign a single crane to each block starting from the top of that list and continue until there are cranes available. Repeat this step until all remaining cranes are assigned.